Applied and Computational Mathematics Seminar

Abstract: Boolean networks have been proposed as models for gene regulation. It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this talk we show that a Boolean network may show extremely chaotic dynamics, even under the simultaneous assumption of several conditions which in randomized studies have been separately shown to correlate with ordered behavior. These properties include using at most two inputs and outputs for every variable, using biased and canalyzing regulatory functions, and restricting the number of negative feedback loops. We also show that networks with all of the above properties can have extremely chaotic dynamics only if a large proportion of variables simply copy previous values of other variables. Such systems share a structural similarity to a relatively small Turing machine acting on one or several tapes. This talk is based on joint work with German A. Enciso from the Harvard Medical School.